1. Field of the Invention
The present invention relates to a computer readable storage medium storing a program for generating reticle data for producing a reticle used in an exposure apparatus, and a method of generating reticle data.
2. Description of the Related Art
A semiconductor device is manufactured by repeating a photolithography process. The photolithography process includes an exposure process of exposing a substrate by illuminating a reticle (also called a mask or original), and projecting the circuit pattern onto a substrate (e.g., a wafer) via a projection optical system. Recent miniaturization of semiconductor devices requires formation of patterns with dimensions smaller than the wavelength of exposure light. However, the formation of such fine patterns is greatly affected by diffraction of light. The contour of a reticle pattern may not be directly formed on a substrate. The pattern may be rounded at the corner or shortened, or the shape accuracy may greatly decrease. To suppress such degradation, the shape of a reticle pattern is corrected. This correction is called optical proximity correction (OPC).
In conventional OPC, the shape of a reticle pattern is corrected by a rule base or a model base using optical simulation, by taking account of the shape of each figure of the reticle pattern and the influence of surrounding patterns.
In the model base using optical simulation, a reticle pattern is deformed until a target pattern is obtained. As the method of deformation, various methods have been proposed. An example is a method (so-called iterative improvement) of, if an optical image is partially expanded, the reticle pattern is narrowed by the any amount, and if the optical image is narrowed, the reticle pattern is expanded by the any amount. While the optical image is recalculated, a formed pattern is gradually deformed to match a target pattern. A method using a genetic algorithm has also been proposed. A method of inserting an auxiliary pattern of a size small enough not to resolve is popular, too.
Japanese Patent Laid-Open No. 2004-221594 discloses a method of determining how to insert an auxiliary pattern by numerical calculation. According to this technique, an interference map is obtained by numerical calculation. A portion where patterns interfere with each other on a reticle and a portion where they cancel each other are derived from the interference map. At a portion where patterns interfere with each other on the interference map, an auxiliary pattern is inserted to make exposure light having passed through the aperture of a main pattern in phase with exposure light having passed through an auxiliary pattern. In the point on the interference map where interference is caused, an auxiliary pattern is inserted so that the phase of exposure light having passed through openings of the contact hole pattern to be transferred and the phase of an exposure light having passed through the auxiliary pattern are equal to each other. At the point on the interference map where interference is canceled, an auxiliary pattern is inserted so that the phase of the exposure light having passed through the openings of the contact hole pattern and the phase of the exposure light having passed through the auxiliary pattern have a difference of 180 degrees. As a result, the contact hole pattern to be transferred and the auxiliary pattern strongly interfere with each other, whereby the target contact hole pattern can be exposed successfully. The interference map amounts light amplitude on the image plane that is positioned in an imaging relation to a reticle plane.
Japanese Patent Laid-Open No. 2008-040470 also discloses a method of numerically obtaining information of an auxiliary pattern. A mask pattern and wafer pattern in a semiconductor exposure apparatus have a partial coherent imaging relationship. In the partial coherent imaging, an aerial image can be calculated by obtaining the coherence on the mask plane from information of an effective light source distribution and performing Fourier integration based on the coherence and the spectral distribution (diffracted light distribution) of a mask. The “coherence” herein mentioned is the degree of interference corresponding to the distance on the mask plane. The “effective light source distribution” is a light intensity distribution formed on the pupil of a projection optical system without any mask.
The coherence of the effective light source can be considered using a transmission cross coefficient (TCC). The TCC is defined by the pupil plane of a projection optical system, and is the portion where the effective light source, the pupil function of the projection optical system, and the complex conjugate of the pupil function of the projection optical system overlap.
According to the method disclosed in Japanese Patent Laid-Open No. 2008-040470, the TCC function is two-dimensionally expressed by fixing the pupil position, thereby obtaining an aerial image. Based on the aerial image, an auxiliary pattern is placed near a peak position expect for a pattern to be resolved.
The interference map in Japanese Patent Laid-Open No. 2004-221594 forms an aerial image when squared, and hence can be regarded as a kind of aerial image.
Circuit patterns can be roughly classified into a line pattern and a contact hole pattern. As patterns are becoming finer and come close to the limit of resolution, it becomes difficult to resolve them.
This is because the contrast is low near the limit of resolution and no desired depth can be attained owing to poor focusing characteristic. As a problem intrinsic to line patterns, the proximity effect is significant and the shape distorts, failing to reproduce an arbitrary shape. Optical proximity correction (OPC) is therefore important for line patterns to correct the shape distortion caused by the proximity effect. In some cases, an auxiliary pattern called SRAF (Sub-Resolution Assist Features) is inserted.
An auxiliary pattern itself is not resolved on the image plane, but interferes with a pattern to be resolved (pattern to be formed on the image plane in accordance with a main pattern), improving the image performance of the pattern to be resolved.
To generate such a reticle pattern, it is easy and effective to insert an auxiliary pattern into a main pattern having undergone optical proximity correction according to the method disclosed in Japanese Patent Laid-Open No. 2004-221594 or 2008-040470.
According to the methods in Japanese Patent Laid-Open Nos. 2004-221594 and 2008-040470, a reticle pattern can be generated based on a given target pattern, illumination conditions (light source shape and polarization), exposure conditions (wavelength, NA, aberration, and magnification), and the like.
However, the illumination conditions are not always optimal for each pattern which forms a reticle pattern. A portion of the pattern that is illuminated under optimal illumination conditions is resolved at high resolution performance. In contrast, a portion of the pattern that is not illuminated under optimal illumination conditions is resolved at only low-resolution performance.
Depending on illumination conditions, the aerial image of an arbitrary line pattern having undergone optical proximity correction has a complicated, wavy shape. If an auxiliary pattern is obtained based on such an aerial image, its shape may become complicated.
Even if a reticle pattern is determined by calculation, no reticle may be produced actually owing to an excessively complicated shape of a fine auxiliary pattern.